4MA0 Higher June 2016 Paper 3 Q12
12 Solve the simultaneous equations
\[\begin{aligned} 4x + 5y &= 13 \\ 3x - 2y &= 27 \end{aligned}\]Show clear algebraic working.
(4)
| Scheme | Marks |
|---|---|
e.g. \(\begin{aligned} &12x + 15y = 39 \\ -\;&12x - 8y = 108 \end{aligned}\) e.g. \(4\left(\dfrac{27 + 2y}{3}\right) + 5y = 13\) | M1 |
| \(23y = -69\); \(y = -3\) | A1 |
| \(12x + 15 \times -3 = 39\) | M1 |
| \(x = 7\); \(y = -3\) | A1 |
| (4) |
Notes
M1: for multiplication to give coefficients of \(x\) or \(y\) the same and correct operation selected to eliminate one variable
(condone any one error in multiplication)
or
for correct rearrangement of one equation followed by correct substitution in the other
A1: cao depends on M1
M1: (dep on 1st M1) for substituting the found variable or starting again to find second variable as M1 above
A1: Award 4 marks for correct values if at least M1 scored